Strengthening the Baillie-PSW primality test
This work addresses the reliability of primality testing for odd composite integers, offering an incremental enhancement to a known method.
The authors tackled the problem of strengthening the Baillie-PSW primality test to reduce false positives, achieving a significant improvement with only five Lucas-V pseudoprimes below 10^15 at almost no extra computational cost.
The Baillie-PSW primality test combines Fermat and Lucas probable prime tests. It reports that a number is either composite or probably prime. No odd composite integer has been reported to pass this combination of primality tests if the parameters are chosen in an appropriate way. Here, we describe a significant strengthening of this test that comes at almost no additional computational cost. This is achieved by including in the test what we call Lucas-V pseudoprimes, of which there are only five less than $10^{15}$.